Progressive Waves in Real Fluids Over a Rigid Permeable Bottom

Abstract

This report deals with the slipping friction in a progressive wave of real fluids propagating over a permeable bottom. Because the “no-slip” condition is usually considered in the wave motion, the horizontal velocity at the seabed is assumed zero. However, based on the numerical simulations and the laboratorial experiment, the slip velocity occurs at the interface as waves pass a permeable bed. It is found that the adherence condition is not suitable for permeable bed. The “overshooting” which is the local maximum horizontal velocity in the wave boundary layer is related to the wave period and the fluid viscosity.Both the linearized Navier-Stokes equation and the slip boundary condition are applied to solve the problem of progressive waves over a permeable bed of finite thickness. In the interface of soil and fluid, the slip velocity is simply assumed to be proportional to the characteristic velocity. Thus, the slipping effect and the permeability of the bottom on the velocity near the seabed can be considered. The linear solutions indicated that the joint effect of slipping friction, permeability and the effect of bottom thickness are crucial for overshooting. Comparing with the experimental results shows that the overshooting phenomena can be explained by this joint effect.